This invention is in the field of digital signal processing methods and particularly relates to digital signal processing of signals acquired in nuclear magnetic resonance (NMR) and like spectral measurements.
Progressively higher resolution NMR measurement demands higher signal to noise performance and a baseline free of artifact and distortion. A known methodology for obtaining improved signal to noise performance involves the sampling of time domain waveforms at a rate in excess of twice the rate corresponding to the highest frequency component of interest in the waveform. This higher than required (oversampling) rate xcfx89s increases the spectral width proportionately and causes the uncorellated noise, or noise from broadband sources to be spread over a wider bandwidth. Only a relatively narrow portion of this expanded bandwidth contains the data of interest. Were the expanded bandwidth to be directly accommodated, the requirement for both memory and time for effecting the Fourier transformation would become impractical or prohibitive. Alternately, and preferably, the oversampled data is subject to a digital filter which returns a single datum from a plurality of oversampled data through convolution of the oversampled data with a selected filter function. Digital filter theory and practice are well known to the artisan.
In the prior art, the use of digital filters commonly introduces artifact and/or distortion to the spectral baseline. An origin for this effect is recognized in the time delays associated with filters which operate upon the time domain waveform. For example, a digital filter initially (at the physical time origin) lacks the requisite history of oversampled data upon which to operate. U.S. Pat. No. 5,652,518, commonly assigned and incorporated herein by reference, treats this initial lack of data by an initialization with use of pseudodata derived from the filter function coefficients to achieve a real-time digital filter exhibiting reduced baseline distortion.
It is known in the prior art to reduce baseline distortion arising from finite response time of filters and delays due to undesired transient instrumental response time through the precise alignment of pseudodata with a time origin. See U.S. Ser. No. 08/723,967, commonly assigned herewith.
It is also a common problem with transient time domain measurements, and particularly in the area of NMR, that the physical time origin is inaccessible for direct sampling. The transient excitation has a finite time width containing the physical time origin. Following the transient excitation, there is usually encountered an interval during which instrumental effects (finite width of the excitation and ringdown of the NMR probe, for example) preclude data acquisition. Thus there is an inaccessible sampling interval resulting in an incomplete data set for data referenced to a physical time origin. Incomplete data sets also occur where the data sampling of a transient waveform is terminated at some point in the waveform evolution leaving unacquired data associated with later times. It is common in such instances to complete the set with null data or resort to sophisticated computational techniques for extrapolation. This latter situation is not the subject of the present invention.
It is known in the prior art to augment an incomplete set of actual data for subsequent treatment, e.g., Fourier transformation, by inclusion of pseudodata points created according to some consistent prescription. Thus, it is a common practice to add a subset of null datums to the actual, but incomplete, data set, as indicated above. The Fourier transformation process is indifferent to the relative position of such data within the data set. Where it is desired to address the problem posed herein, the prior art ""518 patent adds to the data set a subset of pseudodata for which the amplitude of each pseudodatum is prescribed by that digital filter function which is applied to oversampled data. In particular the pseudodata is added at abscissae corresponding to negative time displacements from the physical time origin. For a digital filter of discrete sampling length N=2p +1, there is desirably defined p pseudodatums in this negative time interval. After the elapse of time corresponding to p+1 actual sampling intervals, the digital filter is fully operational to yield a downsampled datum. It is important to recognize that in practice there will be some small number of actual data absent from the oversampled data set in close proximity to the actual time origin, owing to the inaccessibility mentioned above. The number of missing samples and their ordinate values may be supplied by an appropriate procedure which ideally reflects the signal phase and amplitude conditions at t=0.
It is known to estimate pseudo data by methods of linear prediction (LP). These may be broadly described as applications of linear least square methods to actual data for extrapolation into a region where no data has been acquired, such as the above mentioned zone of inaccessibility. In general, LP is computationally intensive, and thus is not suitable for the real time application for which the present invention is preferred. For LP, a substantial number of consecutive actual datums is required to form an acceptable prediction of a pseudodatum by LP for the datum next adjacent to the actual data set. For example, in common practice 2.5 points may be required to obtain the value of the xe2x80x9cnextxe2x80x9d predicted point through LP. In such instances, LP will require formation and inversion of matrices of dimensionality 2.5. Estimate of the next +1 pseudodatum will require similar treatment using a dataset which now includes the pseudodatum formed by the first prediction. Thus error and uncertainty accumulates in a subset of pseudodatums formed by LP methods. Validity of LP methods is established by boundary conditions which produce invariance of spectral parameters between actual data and values produced for such actual data by LP operations. One example of LP utilized in NMR is described by Marion and Bax, Journal of Magnetic Resonance, v. 83, pp. 205-211 (1989). Here, the data are reflected backwards in time for the purpose of obtaining a better estimate for points situated forward in time. These backward reflected pseudodata are then discarded. Other examples of LP are: Gesmar and Hansen, J. Mag. Res., v. A106, pp. 236-240(1994); Barkhuijsen, et al, J. Mag. Res., v. 61, pp.465-481.
In one aspect of the invention, prepending a plurality of pseudo datums to the earliest portion of an oversampled data set establishes a complete data set wherein the pseudodata is derived directly from actual data acquired proximate said pseudodata.
In another aspect of the invention, the actual acquired data is reflected in that time coordinate at which actual data is first available.
In yet another aspect of the invention actually acquired phase resolved data is reflected in that time coordinate at which actual data is first available by taking the complex conjugate of each actual datum and entering said complex conjugate multiplied by a phase factor at a time position symmetrically disposed about that time coordinate with respect to the actual datum.
In still another aspect, said complex conjugate formed pseudodata are multiplied by a selected weighting function g(t).
In another aspect of the invention, a digital filter is employed to reduce the oversampled data acquired at a sampling rate xcfx89s to downsampled data at sampling rate xcfx89s./M.
In still another aspect of the invention, enough pseudodata is prepended to the list of actual data to extend beyond the earliest portion of actual data to a negative time displacement from the time origin by an amount equal to at least approximately {fraction (1/2)} of the length of the digital filter.